Maximal Regularity in Exponentially Weighted Lebesgue Spaces of the Stokes Operator in Unbounded Cylinders

2014/12/18 by Myong‐Hwan Ri, Ri, Myong-Hwan, Reinhard Farwig +1
Mathematics · #35Q30 #76D05 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #FOS: Physical sciences #Mathematical Physics (math-ph) #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1412.5774

openalex publication_date 2014/12/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We study resolvent estimates and maximal regularity of the Stokes operator in L^q-spaces with exponential weights in the axial directions of unbounded cylinders of \Rⁿ,n≥ 3. For a straight cylinder we use exponential weights in the axial direction and Muckenhoupt weights in the cross-section. Next, for cylinders with several exits to infinity we prove that the Stokes operator in L^q-spaces with exponential weights generates an exponentially decaying analytic semigroup and has maximal regularity. The proof for straight cylinders uses an operator-valued Fourier multiplier theorem and unconditional Schauder decompositions based on the \mathcal R-boundedness of the family of solution operators for a system in the cross-section of the cylinder parametrized by the phase variable of the one-dimensional partial Fourier transform. For general cylinders we use cut-off techniques based on the result for straight cylinders and the case without exponential weight.

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